Would the Human Race Use Nuclear Heads Against Huge Asteroids?

When all else has failed.
A bomb might break the asteroid into 2 or more pieces. It would be far better to have 10 smaller impacts spread over a few hours, than one large impact.

Each of the smaller impacts may well be survivable, whereas the single large impact may be an extinction event. Besides, depending on how the asteroid fragments, a significant portion of it may be in tiny pieces that would burn up in the atmosphere.

Hey ... before going for a nuclear solution, we'd really need a "new clear" policy on bombs in space.

Probably not, would be much simpler just to give it shove of about half a degree off line while it was still a few months out that could be done with a nuke without it actually exploding on the surface of the asteroid. Blowing up an asteroid would just turn it from a huge cannon ball to a mass of grape shot.

it's been talked about. might be worth a try, depending on the circumstances

What other chance would we have

"Would the Human Race Use Nuclear Heads Against Huge Asteroids?"

You could use them against stony asteroids, as propulsion, to try and alter their trajectory. Like Project Orion:
https://en.wikipedia.org/wiki/Project_Orion_%28nuclear_propulsion%29

You could shatter an "ice ball", hoping to dissipate the contents across the atmosphere, and let it burn up rather than punch through.

But anything in between, you'd want to use a "gravity tractor", which means you'd want lots of advance warning.

The bomb would have to be drilled deep into the object - and even then it would have debatable effect. In vacuum a nuclear explosion is a flash of light - on Earth the blast is created by the heating of a million tons of atmosphere. Drilled deep in - contained, it flash heats a pocket that (in an ice/rubble impactor) could fracture the impactor.

Gotta get 'em there first... You'd need a large, hefty rocket capable of lofting a 2 to 10 ton device out of Earth orbit - along with a trajectory, and a plan for where to impact it... Normally, a mission like that takes months to years of planning.
I hope we have that kind of time if we ever see one.

Too inefficient.

I could potentially see how that could work bit also consider the dangers. All of the fallout and debris coming to the Earth from it. It would plague the Earth

Only if they were either stupid or desperate.Blowing an asteroid apart into a zillion pieces will mean a much bigger area is is affected when all of those pieces that do not burn up in the atmosphere impact the ground.